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Algebra Discrete Math., 2009, Issue 3, Pages 1–19 (Mi adm125)  

This article is cited in 9 scientific papers (total in 9 papers)

RESEARCH ARTICLE

Partial Hopf actions, partial invariants and a Morita context

Marcelo Muniz S. Alvesa, Eliezer Batistab

a Departamento de Matemática, Universidade Federal do Paraná, Centro Politécnico C.P. 19081, Jardim das Américas 81531–990 Curitiba – PR Brazil Brazil
b Departamento de Matemáatica Universidade Federal de Santa Catarina 88.040–900 Florianópolis–SC Brasil

Abstract: Partial actions of Hopf algebras can be considered as a generalization of partial actions of groups on algebras. Among important properties of partial Hopf actions, it is possible to assure the existence of enveloping actions [1]. This allows to extend several results from the theory of partial group actions to the Hopf algebraic setting. In this article, we explore some properties of the fixed point subalgebra with relation to a partial action of a Hopf algebra. We also construct, for partial actions of finite dimensional Hopf algebras a Morita context relating the fixed point subalgebra and the partial smash product. This is a generalization of a well known result in the theory of Hopf algebras [9] for the case of partial actions. Finally, we study Hopf–Galois extensions and reobtain some classical results in the partial case.

Keywords: partial Hopf action, partial group action, partial smash product, Hopf–Galois extensions.

Full text: PDF file (273 kB)

Bibliographic databases:
MSC: 16W30; 57T05, 16S40, 16S35
Received: 31.08.2009
Revised: 21.09.2009
Language:

Citation: Marcelo Muniz S. Alves, Eliezer Batista, “Partial Hopf actions, partial invariants and a Morita context”, Algebra Discrete Math., 2009, no. 3, 1–19

Citation in format AMSBIB
\Bibitem{AlvBat09}
\by Marcelo~Muniz~S.~Alves, Eliezer~Batista
\paper Partial Hopf actions, partial invariants and a~Morita context
\jour Algebra Discrete Math.
\yr 2009
\issue 3
\pages 1--19
\mathnet{http://mi.mathnet.ru/adm125}
\mathscinet{http://www.ams.org/mathscinet-getitem?mr=2640384}
\zmath{https://zbmath.org/?q=an:1199.16059}


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    Citing articles on Google Scholar: Russian citations, English citations
    Related articles on Google Scholar: Russian articles, English articles

    This publication is cited in the following articles:
    1. Alves Marcelo Muniz S., Batista E., “Globalization Theorems for Partial Hopf (Co)Actions, and Some of their Applications”, Groups, Algebras and Applications, Contemporary Mathematics, 537, ed. Milies C., 2011, 13–30  crossref  mathscinet  zmath  isi
    2. Guo Sh., “on Generalized Partial Twisted Smash Products”, Czech. Math. J., 64:3 (2014), 767–782  crossref  mathscinet  zmath  isi  scopus
    3. Alves Marcelo Muniz S., Batista E., Vercruysse J., “Partial Representations of Hopf Algebras”, J. Algebra, 426 (2015), 137–187  crossref  mathscinet  zmath  isi  elib  scopus
    4. Guo Sh.-j., Wang Sh.-h., “Morita Contexts and Partial Group Galois Extensions For Hopf Group Coalgebras”, Commun. Algebr., 43:3 (2015), 1025–1049  crossref  mathscinet  zmath  isi  scopus
    5. Alves M.M.S., Batista E., Dokuchaev M., Paques A., “Globalization of Twisted Partial Hopf Actions”, J. Aust. Math. Soc., 101:1 (2016), 1–28  crossref  mathscinet  zmath  isi  scopus
    6. Guo Sh., Wang Sh., Wang L., “Partial Representation of Partial Twisted Smash Products”, Publ. Math.-Debr., 89:1-2 (2016), 23–41  crossref  mathscinet  zmath  isi
    7. Chen Q., Wang D., Kang X., “Twisted Partial Coactions of Hopf Algebras”, Front. Math. China, 12:1, SI (2017), 63–86  crossref  mathscinet  isi  scopus
    8. Batista E., “Partial Actions: What They Are and Why We Care”, Bull. Belg. Math. Soc.-Simon Steven, 24:1 (2017), 35–71  mathscinet  zmath  isi
    9. Cavalheiro R., Sant'Ana A., “On the Semiprimitivity and Semiprimality Problems For Partial Smash Products”, Algebr. Colloq., 25:1 (2018), 1–30  crossref  mathscinet  zmath  isi  scopus
  • Algebra and Discrete Mathematics
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